引用本文:刘莉君, 王树勋, 刘丽华.非交换剩余格上模糊极滤子的特征与性质[J].西南大学学报(自然科学版),2019,41(8):58~63
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非交换剩余格上模糊极滤子的特征与性质
刘莉君, 王树勋, 刘丽华
陕西理工大学 数学与计算机科学学院, 陕西 汉中 723000
摘要:
运用模糊集的运算方法和原理,在非交换剩余格上引入了模糊极滤子的概念,并研究了其表示定理和特征性质,获得了在一定条件下非交换剩余格上模糊极滤子与模糊子正蕴涵滤子相互等价的结论.研究结果进一步拓展了非交换剩余格上的模糊滤子理论,为其在逻辑代数及计算机信息处理等方面的应用奠定了理论基础.
关键词:  模糊逻辑  非交换剩余格  模糊滤子  模糊极滤子
DOI:10.13718/j.cnki.xdzk.2019.08.010
分类号:O159
基金项目:国家自然科学基金项目(51505268);陕西省教育厅专项科研项目(17JK0145);陕西理工大学科研项目(SLG1914).
The Characteristics of Fuzzy Fantastic Filters on the Non-Commutative Residuated Lattice
LIU Li-jun, WANG Shu-xun, LIU Li-hua
School of Mathematics and Computer Sciences, Shaanxi University of Technology, Hanzhong Shaanxi 723000, China
Abstract:
By using the principles and methods of fuzzy sets, in this paper, the concept of "fuzzy fantastic filter" is introduced in the non-commutative residuated lattice. By studying its properties and characterizations, the equivalent representation theorems under certain conditions are given between the fuzzy fantastic filter and the fuzzy sub positive implicative filter. The results of the study further extend the fuzzy filter theory of the non-commutative residuated lattice, and lay a theoretical foundation for the application of algebraic logic and computer information processing.
Key words:  fuzzy logic  non-commutative residuated lattice  fuzzy filter  fuzzy fantastic filter
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